Question

which table shows a negative correlation?

x	2	5	6	7	10	12
y	-8	-5	-6	-3	-2	-1
x	2	5	6	7	10	12
y	-5	-5	-5	-5	-5	-5
x	2	5	6	7	10	12
y	6	3	1	1	3	6
x	2	5	6	7	10	12
y	4	2	-4	-3	-11	-12

Explanation:

Step1: Recall negative - correlation concept

In a negative - correlation, as the value of $x$ increases, the value of $y$ decreases.

Step2: Analyze the first table

As $x$ increases ($2,5,6,7,10,12$), $y$ values do not show a consistent decrease. For example, when $x$ goes from $5$ to $6$, $y$ goes from $- 5$ to $-6$ and then from $6$ to $7$, $y$ goes from $-6$ to $-3$.

Step3: Analyze the second table

The $y$ - values are constant ($y=-5$ for all $x$ values), so there is no correlation.

Step4: Analyze the third table

As $x$ increases, $y$ first decreases ($x$ from $2$ to $6$, $y$ from $6$ to $1$) but then increases ($x$ from $6$ to $12$, $y$ from $1$ to $6$), so it is not a negative - correlation.

Step5: Analyze the fourth table

As $x$ increases ($2,5,6,7,10,12$), $y$ consistently decreases ($4,2, - 4,-3,-11,-12$).

Answer:

The fourth table (where $x = 2,5,6,7,10,12$ and $y = 4,2,-4,-3,-11,-12$) shows a negative correlation.